The 26-year-old has been restricted to just three starts since breaking a metatarsal in his right foot in March.
Green had a summer of rest and rehabilitation but the problem flared up again this season and he had another operation last week.
He is expected to return soon after next month's international break.
"It was clear early on that he was a key figure for the side and it was no coincidence when he did miss games at the end of last season, we struggled at times," said Clough. "He is a very important member of the squad. His attitude is terrific. If you get 11 players with the attitude of Paul Green out there, you will not go too far wrong."
The Rams boss added: "He has never been fully fit since March, so we are hoping the latest operation will finally put the matter to rest. It will be lovely to have him fully fit again and it will also be lovely for him to have that nagging doubt removed.
"It has been nagging away at him for too long and we hope this will finally cure it and he can play the last three quarters of the season."